Questions tagged [polyomino]
A geometric puzzle centered around geometric figures formed from unit-squares, or a puzzle that uses polyominoes as an integral part.
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8x8 grid with no unmarked L-pentomino
What is the minimum number of cells on a 8x8 chessboard that need to be marked so that the unmarked cells do not contain an L-pentomino?
An L-pentomino looks like
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Is it possible to arrange the free n-minoes of orders 2, 3, 4 and 5 into a rectangle?
To be explicit, the shapes pictured below, with reflections permitted.
Can these be packed into a rectangle?
This puzzle arose from discussion on r/mathmemes. No solution was posted (and I don't know ...
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A Crabby Sudoku
I present a *deep breath* Even-Odd TetroThermoDoku. From the back of the name to the front:
Rules
Sudoku: Fill each cell with a digit 1-9 such that no number repeats in any row, column, or 3x3 heavy-...
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Gimme five (Pentomino puzzle)
A pentomino is a tile made of five unit squares joined edge to edge. Divide this grid into five pentominoes, each containing the five letters A,B,C,D,E. The regions are not necessarily the same ...
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Hexominos from pentominos, heptominos from hexominos
All twelve pentominoes can be obtained by attaching a single unit square (edge to edge) to one of the squares that make up one (or more) of the following four tetrominoes:
a) What is the least number ...
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Tiling a 5-by-5 bathroom with L-shaped triomino tiles
The following puzzle appeared in the Cambridge, UK February 2024 MathsJam Shout:
Tiling with Triominoes
Imagine tiling a 5-by-5 bathroom with L-shaped triomino tiles.
Clearly, not every square can be ...
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Which heptomino is it obvious can't tile the plane?
A polyomino is a collection of equal-sized squares joined edge-to-edge in the plane (think Tetris pieces, but with an arbitrary number of squares instead of just four). A heptomino is a polyomino ...
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Yet another pentomino puzzle
Just rearrange the 13 checkered polyominoes shown below to form a chessboard. The solution is unique and unusual.
Clarification: The pieces may be reflected; the coloring on the back is as if the ink ...
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Making a 3 x 8 grid with tetrominoes
I'm wondering if it is possible to make a 3x8 grid using 6 tetrominoes: 2 Is, 2 Ls, a Z skew, and a square tetromino. I believe it may be impossible but would like to know why.
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Xmas-colored tiles
If you subdivide a 2x2 tile into 4 unit squares and then color each unit square either red or green, then there are $2^4=16$ ways you can do this as shown below:
Can you use all 16 tiles (rotations ...
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Ziggy - Can you make a square from 49 polyomino pieces
This puzzle is variant of the puzzle Ziggy - Make a square from 8 polyomino pieces by jaap-scherphuis.
This puzzle is based on the fact that $1+2+3+\cdots+49=35^2$. It consists of 49 zigzag polyomino ...
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Polyomino equation part 2
There is a particular shape (holes are permitted) that you can build with four copies of the piece on the left, or with 5 copies of the piece on the right. You may rotate and flip the pieces, but ...
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The Diamond of Columbus
There are up to flipping / rotation 12 distinct pentominoes.
Can you fit them without overlap in the white area?
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Polyomino equation
There is a particular shape (holes are permitted) that you can build with three copies of the piece on the left, or with 5 copies of the piece on the right. You may rotate and flip the pieces, but ...
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